01 - Rinse the corned beef brisket thoroughly under cold running water to remove excess brine. Pat dry with paper towels and place the brisket fat side up in the bottom of a 6-8 quart slow cooker.
02 - Open the spice packet included with the corned beef and sprinkle the spices evenly over the surface of the brisket. If using Dijon mustard, spread 1 tablespoon over the meat to help the spices adhere.
03 - Arrange the onion quarters, smashed garlic cloves, carrot chunks, potato pieces, bay leaves, and peppercorns around and on top of the brisket, distributing them evenly in the cooker.
04 - Pour the beef broth and water over the ingredients, ensuring the liquid nearly covers the meat and vegetables.
05 - Cover the slow cooker with the lid. Cook on LOW setting for 8 hours, or until the meat is fork-tender and easily pulls apart when tested with a fork.
06 - During the last 2 hours of cooking time, carefully nestle the cabbage wedges down into the cooking liquid around the brisket and vegetables. Cover and continue cooking until the cabbage is tender but not mushy.
07 - Using tongs, carefully transfer the corned beef to a cutting board. Let it rest for 10 minutes to allow the juices to redistribute. Slice the brisket thinly against the grain for maximum tenderness.
08 - Arrange sliced corned beef on serving plates alongside the tender vegetables. Ladle some of the cooking broth over each portion for added moisture and flavor. Serve immediately while hot.